Dual-lumen or multi-lumen medical devices are typically employed to deliver different drugs, blood products, nutritional fluids, or other fluids into the vascular system, peritoneal or epidural space, or other locations within a patient body. Accordingly, it is medically desirable to manage contemporaneous fluid communications between such medical devices and a plurality of fluid sources. Furthermore, it has also been long recognized to be medically desirable to control fluid flow in a pressure responsive fashion to prevent undesired fluid flows that usually cause leakage and blood clotting. Pressure Activated Safety Valve Technology available under the trademark PASV® Valve Technology from Boston Scientific Corporation, Natick, Mass., has been employed in medical devices to control fluid flow. A single lumen pressure responsive slit valve housing is described in U.S. Pat. Nos. 5,169,393, 5,205,834, and 5,843,044, the entire contents of each of which are incorporated herein by reference. Such a single lumen design, however, has a limited ability to accommodate a dual-lumen or multi-lumen medical device. For example, use of a single lumen valve housing in a dual lumen port requires clumsy intermediate connectors to accommodate fluid flow from spatially separated lumens into the side-by-side configuration necessitated by the dimensions of a multi-lumen catheter. This intermediate connector structure is cumbersome, subject to leakage and compromises the sterility of the fluids flowing therein. Naturally, this also complicates the process of manufacture and assembly, and increases its cost, as well as increases the chances of structural failure.